Triangle area calculation

The isosceles triangle XYZ has a base of z = 10 cm. The angle to the base is the sum of the angles at the base. Calculate the area of the triangle XYZ.

Final Answer:

S =  25 cm²

Step-by-step explanation:

$$\begin{gathered} z=10\text{cm} \\ A+B+B=180 \\ A=B+B \\ A+2B=180 \\ A-2B=0 \\ Row2-Row1\to Row2 \\ -4B=-180 \\ B=\frac{-180}{-4}=45 \\ A=180-2B=180-2\cdot 45=90 \\ A=90 \\ B=45 \\ {S}_1=z^2=10^2=100{\text{cm}}^2 \\ S=\frac{S_1}{4}=\frac{100}{4}=25{\text{cm}}^2 \end{gathered}$$

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